Question

Jeni is painting a flattened shoebox for a school project. The shoebox measures 72.5 cm x 47.5 cm x 104 cm. What is one area that would be identified on the box’s net?(1 point)
Responses

224 cm2
224 cm squared

358,150 cm2
358,150 cm squared

7,540 cm2
7,540 cm squared

31,847.5 cm2

Answer 1

To find the area that would be identified on the shoebox's net, we need to calculate the surface area of the shoebox. A shoebox is a rectangular prism, and the surface area can be calculated using the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where:
- \( l \) = length (104 cm)
- \( w \) = width (72.5 cm)
- \( h \) = height (47.5 cm)

Let's calculate:

1. \( lw = 104 \times 72.5 = 7,540 \, \text{cm}^2 \)
2. \( lh = 104 \times 47.5 = 4,930 \, \text{cm}^2 \)
3. \( wh = 72.5 \times 47.5 = 3,447.5 \, \text{cm}^2 \)

Now, add these areas together:

\[
lw + lh + wh = 7,540 + 4,930 + 3,447.5 = 15,917.5 \, \text{cm}^2
\]

Now, multiply this sum by 2 to find the total surface area:

\[
\text{Surface Area} = 2 \times 15,917.5 = 31,835 \, \text{cm}^2
\]

It seems there was a small error in the calculation of individual areas, let's double check:

- \( lw = 104 \times 72.5 = 7,540 \, \text{cm}^2 \) (Correct)
- \( lh = 104 \times 47.5 = 4,930 \, \text{cm}^2 \) (Correct)
- \( wh = 72.5 \times 47.5 = 3,447.5 \, \text{cm}^2 \) (Correct)

So, the total surface area calculation is indeed:

\[
\text{Surface Area} = 2(7,540 + 4,930 + 3,447.5) = 2 \times 15,917.5 = 31,835 \, \text{cm}^2
\]

Thus, the closest answer from your options is:

31,847.5 cm²

So the correct response is **31,847.5 cm²**.